43. Refer to Exercise 1 and answer the following questions:

a. Given that X  1, determine the conditional pmf of Y that is, , , and

.

b. Given that two hoses are in use at the self-service island, what is the conditional pmf of the number of hoses in use on the full-service island?

c. Use the result of part

(b) to calculate the conditional probability

d. Given that two hoses are in use at the full-service island, what is the conditional pmf of the number in use at the self-service island?